Filtering with State-Observation Examples via Kernel Monte Carlo Filter
Filtering with State-Observation Examples via Kernel Monte Carlo Filter
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DOI：
10.1162/neco_a_00806
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发表时间：
2013-12
影响因子：
2.9
通讯作者：
Motonobu Kanagawa;Yu Nishiyama;A. Gretton;K. Fukumizu
中科院分区：
文献类型：
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作者：
Motonobu Kanagawa;Yu Nishiyama;A. Gretton;K. Fukumizu
这封信解决了用状态空间模型过滤的问题。用于过滤的标准方法假设观测的概率模型（即，观察模型）被明确地或至少参数化地给出。我们考虑一个设置，这个假设是不满足的，我们假设的观测模型的知识只提供了状态观测对的例子。此设置很重要，当状态变量被定义为与观测值非常不同的量时会出现。我们提出了核蒙特卡罗滤波器，一种新的过滤方法，专注于这种设置。我们的方法是基于核均值嵌入的框架，这使得非参数后验推理使用状态观测的例子。该方法将状态分布表示为加权样本，通过采样传播这些样本，利用核贝叶斯规则估计状态后验，并通过核羊群重新采样。特别是，采样和重新采样的过程是新颖的，在使用核均值嵌入表示，所以我们从理论上分析他们的行为。我们揭示了以下性质，这是类似于粒子方法中的相应程序：采样的性能可以降低，如果加权样本的有效样本大小是小的，和resception提高采样性能，通过增加有效样本大小。我们首先证明这些理论研究结果的合成实验。然后，我们通过人工和真实的数据实验，其中包括基于视觉的移动的机器人定位的有效性所提出的过滤器。
This letter addresses the problem of filtering with a state-space model. Standard approaches for filtering assume that a probabilistic model for observations (i.e., the observation model) is given explicitly or at least parametrically. We consider a setting where this assumption is not satisfied; we assume that the knowledge of the observation model is provided only by examples of state-observation pairs. This setting is important and appears when state variables are defined as quantities that are very different from the observations. We propose kernel Monte Carlo filter, a novel filtering method that is focused on this setting. Our approach is based on the framework of kernel mean embeddings, which enables nonparametric posterior inference using the state-observation examples. The proposed method represents state distributions as weighted samples, propagates these samples by sampling, estimates the state posteriors by kernel Bayes’ rule, and resamples by kernel herding. In particular, the sampling and resampling procedures are novel in being expressed using kernel mean embeddings, so we theoretically analyze their behaviors. We reveal the following properties, which are similar to those of corresponding procedures in particle methods: the performance of sampling can degrade if the effective sample size of a weighted sample is small, and resampling improves the sampling performance by increasing the effective sample size. We first demonstrate these theoretical findings by synthetic experiments. Then we show the effectiveness of the proposed filter by artificial and real data experiments, which include vision-based mobile robot localization.